Isospin Dynamics in Iridates revealed by Resonant inelastic x-ray scattering The Advanced Photon Source is funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Advanced Photon Source 9700 S. Cass Ave. Argonne, IL USA 5d transition metal L edge RIXS spectroscopy Abstract Jungho Kim 1, T. Gog 1, D. Casa 1, A. Said 1, M. Upton 1, Y.-J. Kim 2, B. J. Kim 3, J. F. Mitchell 3, M. van Veenendaal 1, G. Khaliullin 4, M. Daghofer 5, G. Jackeli 4, J. van den Brink 5 1 XSD, APS, ANL, Argonne, Illinois, USA. 2 Dept. of Phys., Univ. of Toronto, Toronto, Ontario, CA. 3 MSD, ANL, Argonne, Illinois, USA. 4 MPI for Solid State Research, Heisenbergstrae 1, Stuttgart, DE. 5 Inst. for Theo. Solid Sate Phys., IFW Dresden, Helmholtzstrasse 20,Dresden, DE. Sr 2 IrO 4 Sr 3 Ir 2 O 7 Iridium oxides with strong relativistic spin-orbit coupling have received much attention due to intriguing sets of novel electronic and magnetic phases and phenomena, which were imagined for a long time but not realized in real world. Among many materials, Sr 2 IrO 4 and Sr 3 Ir 2 O 7 provide model cases for investigating essential aspects of the magnetic exchange interactions of the so- called J eff isospin states. We present momentum-, and energy-resolved measurements of collective excitations of the spin-orbit coupled composite states in iridium oxide materials by resonant inelastic x-ray scattering (RIXS). The J eff =1/2 isospin dynamics of Sr 2 IrO 4 can be well described by the isotropic Heisenberg model. The dynamics of d-d excitations across the spin-orbit coupling split levels mirrors the fundamental process of an analogous one-hole propagation in a background of ordered spins which renders the low-energy effective physics of Sr 2 IrO 4 much akin to that in superconducting cuprates. The J eff =1/2 isospin dynamics of of Sr 3 Ir 2 O 7 shows a marked departure from the Heisenberg model due to the strongly enhanced bond-directional pseudodipolar interactions, which are essential for a realization of the Kitaev model in a honeycomb lattice with a spin-liquid ground state. A. Said Si 844 Analyzer Measurement [1] Momentum/Energy-resolved spectra of collective excitations Current energy resolution ~ 30meV Iridium oxides spin up l z =0 spin down l z =1 J eff =1/2 Isospin [2] Exchange interactions in square lattice [2] HeisenbergPseudodipolar Strong Spin-Orbit couplings OIr [1] S. Huotari, et al., J. Synchrotron Radiat. 12, 467 (2005); ibid, Rev. Sci. Instrum., 77 (2006). Yu. V. Shvyd’ko et al., J. Electron Spectrosc. Relat. Phenom. (2012). T. Gog, et. al., J. Synchrotron Rad. 20, 74 (2013). [2] B. J. Kim, et. al., Phys. Rev. Lett. 101, (2008). B. J. Kim, et.al., Science. 323, 1329 (2009). G. Jackeli and G. Khaliullin PRL 102, (2009). [3] N. S. Headings, et. al., Phys. Rev. Lett. 105, (2010). [4] Jungho Kim, et. al., Phys. Rev. Lett. 108, (2012). [5] Jungho Kim, et. al., Phys. Rev. Lett. 109, (2013). J. W. Kim, et.al., Phys. Rev. Lett. 109, (2013). [6] K. M. Shen, et. al., PRL 93, (2004). B. J. Kim, et. al., Phys. Rev. Lett (2008). P. D. C. King, et. al., Phys. Rev. B (R) (2013). W. Chen, et. al., Phys. Rev. B 80, (2009). [7] P. A. Lee, et al., Rev. Mod. Phys. 78, 17 (2006). S. Schmitt-Rink, et al., Phys. Rev. Lett. 60, 2793 (1988). [8] O. P. Sushkov, et al., Phys. Rev. B 56, (1997). S. LaRosa et al., Phys. Rev. B 56, R525 (1997). t 2g band  J eff = 1/2 band J eff = 3/2 band  SO Spin-orbit coupling splits the t 2g band t 2g has effective angluar momentum L eff =1  UHB LHB  SO U J eff = 1/2 UHB J eff = 1/2 LHB J eff = 3/2 band Small U with AFM can induce Mott transition Nature of Insulating gap and Mott state [2]       Energy loss (eV) Magnon creation after the RIXS process ✔ Single band Mott Hubbard ✔ 2D square lattice ✔ Spin ½ La 2 CuO 4 : Parent compound of High-T C Superconductors Sr 2 IrO 4 Neutron [3] RIXS [4] J JcJc J c-axis collinear antiferromagnetic structure [5] Large magnon gap Larger window for the collinear AF in Sr 3 Ir 2 O 7 due to the isotropic wavefunction of isospins. Large magnon gap due to large η=J H /U with large  Spin-orbiton creation after the RIXS process Initial state Intermediate state final state Missing quasiparticles in ARPES of Sr 2 IrO 4 [6] Resolution improvement and observation of sharp exciton Two scenarios Franck-Condon broadening of the spectral functions the strong interactions between holes and optical phonons. Charged (Coulomb) defects ✔ Charge neutral  Less lattice deformation and so less Frank- Condon broadening and no effects from Coulomb defects. ✔ Bulk-sensitive  Immune to the surface defects Heisenberg exchange interaction (J=60, J 1 =-20, J 2 =15meV) Strongly enhanced bond-directional pseudodipolar interactions RIXS matrix elememts and selective probe t-J model analogy [7] : hole vs spin-orbiton Orbital exciton by RIXS is a better realization of the t-J model than ARPES Selective mapping of the two exciton modes and their comparison to SCBA calculations. [7] Asymmetric quasiparticle intensity [8] : A generic feature predicted for a hole in a t-J model and indirectly inferred from ARPES measurements on cuprates, which possibly accounts for the Fermi arc observed in the doped case as due to the strongly suppressed shadow band intensity. ….…. Quantum spin-liquid Topological insulator Development of Novel Analyzer System for RIXS with better than 10 meV resolution Si-based collimation-dispersion-selection (CDS) analyzer combined with collimating multilayer mirrors Achieve energy resolution 2-20 meV for any hard x-ray energy and balance the resolution with flux to provide practical counts. Take RIXS energy resolution to a level competitive with neutron spectrometers, the current ‘gold standard’ for inelastic scattering with a capability to study far smaller (sub-mm) or thin-film samples. Compatible with a conventional scattered photon polarization analyzer. Augment the APS upgrade project, which is to provide an unprecedented combination of high-energy, high-brilliance, and nano-scale focal spots for modern scientific and technological research. Si-based collimation-dispersion-selection (CDS) analyzer combined with collimating multilayer mirrors Achieve energy resolution 2-20 meV for any hard x-ray energy and balance the resolution with flux to provide practical counts. Take RIXS energy resolution to a level competitive with neutron spectrometers, the current ‘gold standard’ for inelastic scattering with a capability to study far smaller (sub-mm) or thin-film samples. Compatible with a conventional scattered photon polarization analyzer. Augment the APS upgrade project, which is to provide an unprecedented combination of high-energy, high-brilliance, and nano-scale focal spots for modern scientific and technological research. Greatly improved tails of resolution function compared to conventional spherical analyzers. References Full dynamics of J eff =1/2 isospin revealed by RIXS